Bring a large pot of heavily salted (about 2 tablespoons) water to a boil. Add the 2 bunches mustard greens and cook until just wilted (about 1 minute). Transfer with kitchen tongs to a baking sheet and spread into a single layer to cool. Chop into bite-sized pieces and set aside.
Return water in the pot to a boil, add the 1 pound spaghetti. Cook 4 minutes (pasta will not be cooked all the way, it will finish cooking in the wine). Reserve 1 cup of pasta water. Drain pasta through a colander and return empty pot to stove.
Add the bottle of wine and 1 tablespoon sugar to pot, bring to a boil and reduce by half, about 8 to 10 minutes. Add the pasta and gently stir with tongs to break apart the strands. Boil over high heat until most of the liquid is absorbed and pasta is al dente, about another 2-3 minutes.
Meanwhile, heat oil in a large frying pan over medium-high heat. Add garlic and season with 1 teaspoon salt. Add the mustard greens and 1 teaspoon pepper flakes. Cook, stirring occasionally until greens are coated in oil and garlic is golden. Add half of the reserved water and stir to combine.
Add mustard greens mixture to the pasta and toss gently. Add more of the pasta water if spaghetti is too dry. Serve with cheese and more red chile flakes, if desired.